In many technical fields, linearization of a nonlinear element is used to compensate for unwanted effects caused by the nonlinear behaviour of the nonlinear element. One possibility to linearize a nonlinear element is to predistort the signal input into the nonlinear element to ensure that the output signal of the nonlinear element is, in the ideal case, linearly related to the input signal of the predistorter.
In general, such predistorter is a highly complex nonlinear system which incorporates memory. An important step in predistortion is the identification of the nonlinear element based on input-output measurements. Once the nonlinear element has been identified, it may prove possible to calculate appropriate predistorter parameters for linearization of the system containing the predistorter and the nonlinear element.
The technique of predistortion is widely used in modern wireline and wireless communication systems. Typically, communication systems employ a power amplifier with high output power requirements. Such power amplifiers are often driven in the nonlinear region to obtain the highest possible efficiency. This leads in general to spectral regrowth and intermodulation distortion in the signal band. Basically, there are two approaches to minimize these unwanted effects. The first one is the employment of an oversized power transistor which is purely driven in the linear range even for maximum output power requirements. This approach is highly cost intensive during production and also during operation because of the high price of such transistor and its low signal to DC efficiency. The second approach, signal predistortion, allows to create low price devices fulfilling a given spectral mask for the transmission signal even though the power amplifier is driven in the nonlinear region.
Identification of the nonlinear power amplifier or, more general, the nonlinear element is usually accomplished at a sufficiently high sampling rate to cover the information in the out-off-band region caused by the nonlinearity. Usually, the sampling frequency for identification of the nonlinear element is at least twice the bandwidth of the ouput signal, i.e. 2P-times higher than the signal bandwidth at the input of the nonlinear element, where the factor P denotes the highest odd-order nonlinearity of the nonlinear element. Because the nonlinear behaviour of the nonlinear element is generally unknown before identification, high sampling rates of a few hundreds of Msamples/s are used in communication applications.
According to a generalized sampling theorem, it is possible to uniquely identify a nonlinear element on a sampling frequency which is twice the input signal bandwidth or, in other words, which can satisfy the Nyquist theorem for the input signal of the nonlinear element.